What is the ruling of Islamic law on a deceased person's debt being paid from his friend's private money, given that the heirs have refused to pay due to the absence of clear proof of the debt?

The merchant's action of settling his friend's debt and relieving his distress is commendable in Islamic law, due to the Prophet's (peace and blessings be upon him) saying: "A Muslim is the brother of a Muslim. He does not wrong him, nor does he hand him over. Whoever fulfills the need of his brother, Allah will fulfill his need. Whoever relieves a Muslim of a distress, Allah will relieve him of a distress from the distresses of the Day of Resurrection." The most beloved of people to Allah are those most beneficial to people, and the most beloved of deeds to Allah is joy that you bring to a Muslim, or relieving him of distress, or settling his debt.